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February 24, 20260 citationsOpen Access

Universal Grid Mechanics (UGM):An Axiomatic, Admissibility-First Framework for Physical Reality

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GVGabriel Toledo VillarroelGVGabriel Toledo VillarroelGVGabriel Toledo Villarroel

Key Points

  • This work aims to establish Universal Grid Mechanics as a foundational framework for understanding physical reality.
  • Introduced an axiomatic foundation with a small set of ontological axioms.
  • Developed a mechanism for coherence selection to ensure outcome stability.
  • Defined a non-spacetime admissibility metric for physical states.
  • Provided an empirical touchpoint for testing the framework's falsifiability.
  • Motion, forces, time, and observable objects derive from the grid's stress dynamics.
  • Singularities and infinities are effectively excluded through axiomatic design.
  • Quantitative examples and full mathematical derivations are included in additional technical work.

Abstract

Universal Grid Mechanics (UGM) proposes that physical reality is not fundamentally composed of particles, fields, or spacetime, but of a continuous underlying structure: the grid, that can deform, store stress, and update itself. Instead of beginning with equations, UGM begins with a small set of ontological axioms that determine which physical states are physically admissible. Motion, forces, time, and observable objects arise as consequences of how stored stress relaxes within this grid under local interaction. Singularities and infinities are excluded by construction, rather than repaired after the fact. This paper presents the axiomatic foundation of UGM, the primitive update elements, a coherence–selection mechanism governing outcome stability, a non-spacetime admissibility metric, and a concrete empirical touchpoint illustrating falsifiability. Quantitative instantiations and full mathematical derivations are presented in companion technical work.

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Cite This Study

Villarroel et al. (2026) studied this question.

synapsesocial.com/papers/699d3fb3de8e28729cf64707https://doi.org/10.5281/zenodo.18529620
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  4. 4UGM00 as the High-Resolution Predictive Regime of Universal Grid Mechanics2026
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